Atmospheric Circulation ofhot Jupiters
Adam Showman
University of Arizona
Collaborators: Nikole Lewis, Tad Komacek, Jonathan Fortney,Lorenzo Polvani, Yuan Lian, Mark Marley, Yohai Kaspi, TiffanyKataria

Exoplanets: an exploding new field•

Over 3500 known extrasolar planets•

Nearly 700 planets have been detected with the “Doppler” method•

Nearly 2700 planets have been detected with “transit” method (plus many Kepler
candidates):

Together, these give the planetary mass, radius, and orbital properties.

•~50 planets discovered by direct imaging:Planet mass vs. year of discovery

Planet radius vs. year of discovery

Planet mass vs. semi-major axis

exoplanet.eu

Hot Jupiters: Spitzer light curves for HD 189733b

Knutson et al. (2007, 2009)

8 mm

24 mm

Lightcurves for hot Jupiters

WASP-19b (Wong et al. 2016)

WASP-43b (Stevenson et al. 2014)

HD209458b (Zellem et al. 2014)

WASP-18b (Maxted et al. 2013)

Dependence of day-night flux contrast on effective temperature

Komacek et al. (2017)

Motivating questions• What are the fundamental dynamics of the highly irradiated “hot Jupiter”
circulation regime? Can we explain lightcurves of specific hot Jupiters?
What is the mechanism for displacing the hottest regions to the east?

• What are mechanisms for controlling the day-night temperature contrast on
hot Jupiters? Can we explain the increasing trend of day-night flux contrast
with incident stellar flux?

• What controls the cloudiness of hot Jupiters?
• How do circulation regime---and observables---of hot Jupiters vary withparameters like incident stellar flux and rotation rate?

Hot Jupiter circulation models typically predict several
broad, fast jets including equatorial superrotation

Knutson et al. (2007)

Showman et al. (2009)

Heng et al. (2011)

Rauscher & Menou (2012)

Showman &Guillot (2002)

Knutson et al.
(2007)WASP-43b

HD 209458b
Kataria et al. (2015)

Showman et al. (2009),
Knutson et al. (2012)

HD 189733b

Showman et al. (2009),
Zellem et al. (2014)

Comparisons of data to GCMs

What causes the equatorial superrotation?
Hide’s theorem: Superrotating equatorial jets (corresponding to local
maxima of angular momentum) cannot result from axisymmetriccirculations (e.g., angular-momentum conserving Hadley cells).
Such jets must instead result from up-gradient momentum transport
by waves and/or turbulenceThis is a fairly common phenomenon in turbulence… the question is, in thepresent context, what is the specific mechanism?

Simple models to isolate superrotation mechanism• To capture the mechanism in the simplest possible context, adopt theshallow-water equations for a single fluid layer:
hheq - h¶h+ Ñ × (hv) =º Qh¶tt radRadiatively activeatmosphere
Deep atmosphereand interior

where (heq-h)/trad represents thermal forcing/damping, -v/tdrag represents
drag, and where d=1 when Qh>0 and d=0 otherwise• First consider linear, steady analytic solutions and then consider full
nonlinear solutions on a sphere.

The day/night thermal
forcing induces standing
planetary-scale (Rossbyand Kelvin) waves, whichtransport momentum to theequator. This induces
superrotation.

Showman & Polvani (2011), ApJ 738, 71

Linear analytic calculation

Full nonlinear numerical solutions on a sphere

Low amplitude(~linear)High amplitude(non-linear)Showman & Polvani (2011)

Showman & Polvani (2011)

This Rossby/Kelvin wave pattern is clearly evident in
spin-up phase of 3D hot Jupiter simulations

Leading limb

Average during transit

Trailing limb

Showman et al. (2013a)

A direct detection of the equatorial jet has recently
been made, and is consistent with GCM predictions.

Louden & Wheatley (2015)

Doppler detection of equatorial jetToward predictive theories of the circulation• GCM simulations are useful but by themselves do not imply
understanding• The ultimate goal is to understand the mechanisms and obtain apredictive theory for the day-night temperature differences, verticalmixing rates, and other aspects of the circulation.

It is commonly assumed that day-night temperature differences aresmall if trad >> tadvect and temperature differences are large if
trad << tadvect .

• Problems: This is not predictive, since tadvect depends on the flow. It
also neglects a role for other important timescales in the problem,including wave, frictional, and rotational timescales. These almost
certainly matter.

Weak damping (trad = 10 days),
relevant to cool planets

From Warm toVery Hot Jupiters

Moderate damping (trad = 1 day),relevant to warm planets

Strong damping (trad = 0.1 days),relevant to hot planets

Showman et al. (2013a)

Komacek & Showman (2016);
seealso Perez-Becker & Showman (2013)

Hot-Jupiter circulation in idealized GCM simulations as a function of radiative
time constant and strength of frictional dragTheory for day-night temperature contrast
Day-night thermal contrast from afully predictive theory with zero
free parameters and no tuning

The theory matches the simulation results well over a multi-order-of-magnitude
parameter space in the radiative and frictional time constants.

The theory shows that the transition between regimes is generally controlled bywave adjustment (and the resulting vertical advection) rather than horizontal
advection timescales.

Komacek & Showman (2016);
seealso Perez-Becker & Showman (2013)

Day-night thermal contrast fromthree-dimensional GCM
simulations

Komacek & Showman (2016)

Day-night temperature differences vs pressure

Curves:Solid=GCM
Dotted=theory

Waves adjust isentropes up
or down in an attempt toflatten them. This erases
horizontal temperature
differences.

This is a key mechanism for
maintaining the small
longitudinal temperaturedifferences in Earth’s
tropics: the “weaktemperature gradient” orWTG regime.

Showman et al. (2013b), “Atmospheric circulation of terrestrial exoplanets,” submitted
to Comparative Climatology of TerrestrialPlanets, Univ. Arizona Press (to be published)

Wave adjustment process

The model explains the emerging observational trend

Komacek et al. (2017), Perez-Becker & Showman (2013)

What about objects cooler than “classical” hot Jupiters?
• Despite the focus on hot Jupiters, known EGPs populate a continuum from~0.03-0.05 AU to > 1 AU

• Such “warm” Jupiters will rotate non-synchronously:6æöæö
Qat spindown » 10 6 ç 5 ÷ç orb ÷ yr
è10 øè 0.05AU ø• Fundamental questions also exist about how the circulation on hot Jupiters
relates to that on Jupiter, Earth, and brown dwarfs

All of this motivates an investigation of how hot Jupiter circulation regimes-and observables--vary with incident stellar flux and rotation rate

A regime shift from hot to warm Jupiters?

Showman, Lewis & Fortney (2015)

Showman, Lewis & Fortney (2015)

Predicted regimes
0.2 AU

8.8 day0.5 day

0.03 AU

Showman, Lewis & Fortney (2015)

Orbital distance

0.2 AU

0.03 AU0.5 day

Rotation period

8.8 day

Showman, Lewis, & Fortney (2015)

Orbital distance

0.2 AU

0.03 AU0.5 day

Rotation period
8.8 dayObservational predictions: IR light curves

Orbital distanceShowman, Lewis, & Fortney (2015)

0.2 AU

0.03 AU0.5 day

Rotation period

8.8 dayObservational predictions: IR spectra

Orbital distanceShowman, Lewis, & Fortney (2015)

0.2 AU

0.03 AU0.5 day

Rotation period

8.8 dayDynamical themes•

The typical hot Jupiter is in the “all tropics” regime where equatorial (e.g., Kelvinand Rossby) waves adjust the temperature structure in the longitude direction, andmeridional (“Hadley”) circulations adjust it in latitude.

•Breakdown of the wave adjustment allows large day-night temperature differenceson particularly close-in hot Jupiters.

•Standing equatorial (Kelvin and Rossby) waves triggered by the day-night thermal
forcing transport momentum to the equator, causing equatorial superrotation.

•Rapidly rotating EGPs will have both tropics and an extratropics, with heattransport at high latitudes controlled by baroclinic instabilities, with large equatorpole temperature differences and zonal-mean winds peaking in midlatitudes.
Lightcurves may allow constraints on rotation rates for non-synchronously rotating
planets.

Approach to constructing a theory
Thermodynamic energy equation:

Approach to constructing a theory
Thermodynamic energy equation:
Here, variables are:
DT=day-night temperature difference
U=horizontal wind speed
W=vertical wind speed

Goal: solve analytically for DT, U, and W as a function of control parameters(trad, tdrag, rotation rate, planetary radius, etc)

Approach to constructing a theory
Thermodynamic energy equation:
Here, variables are:
DT=day-night temperature difference
U=horizontal wind speed
W=vertical wind speed

Momentum equation:

Goal: solve analytically for DT, U, and W as a function of control parameters(trad, tdrag, rotation rate, planetary radius, etc)

Approach to constructing a theory
Thermodynamic energy equation:
Here, variables are:
DT=day-night temperature difference
U=horizontal wind speed
W=vertical wind speed

Momentum equation:

Goal: solve analytically for DT, U, and W as a function of control parameters(trad, tdrag, rotation rate, planetary radius, etc)

Approach to constructing a theory
Thermodynamic energy equation:
Here, variables are:
DT=day-night temperature difference
U=horizontal wind speed
W=vertical wind speed

Momentum equation:

Continuity equation:

Goal: solve analytically for DT, U, and W as a function of control parameters(trad, tdrag, rotation rate, planetary radius, etc)

References1
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Heng, K., Menou, K., Phillipps, P.J., 2011: Atmospheric circulation of tidally locked
exoplanets: a suite of benchmark tests for dynamical solvers, MNRAS, 413, 2380-2402.
Kataria, T., Showman, A.P., Fortney, J.J., Stevenson, K.B., Line, M.R., Kreidberg, L.,
Bean, J.L., Désert, J.-M., 2015: The atmospheric circulation of the hot Jupiter WASP-43b:
Comparing three-dimensional models to spectrophotometric data, Astrophys. J., 801, 86.
Knutson, H.A., Charbonneau, D., Allen, L.E., Fortney, J.J., Agol, E., Cowan, N.B.,
Showman, A.P., Cooper, C.S., Megeath, S.T, 2007: A map of the day-night contrast of theextrasolar planet HD 189733b, Nature, 447, 183-186.
Knutson, H.A., Charbonneau, D., Cowan, N.B., Agol, E., Showman, A.P., Fortney, J.J.,
Henry, G.W., Everett, M.E., Allen, L.E., 2009: Multi-wavelength constraints on the daynight circulation patterns of HD 189733b, Astrophys. J., 690, 822-836.
Knutson, H.A., Lewis, N., Fortney, J.J., Burrows, A., Showman, A.P., Cowan, N.B., Agol,E., Aigrain, S., Charbonneau, D., Deming, D., Désert, J.-M., Henry, G.W., Langton, J.,
Laughlin, G. 2012: 3.6 and 4.5μm phase curves and evidence for non-equilibrium
chemistry in the atmosphere of extrasolar planet HD 189733b, Astrophys. J., 754, 22.
Komacek, T.D., Showman, A.P., 2016: Atmospheric circulation of hot Jupiters: Daysidenightside temperature differences, Astrophys. J., 821, 16.
Komacek, T.D., Showman, A.P., Tan, X., 2017: Atmospheric circulation of hot Jupiters:
Dayside-nightside temperature differences. II. Comparison with observations, Astrophys.
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References2••••••••

Louden, T., Wheatley, P.J., 2015: Spatially resolved eastward winds and rotation of HD
189733b, Astrophys. J. Lett., 814, L24.
Maxted, P.F.L., Anderson, D.R., Doyle, A.P., Gillon, M., Harrington, J., Iro, N., Jehin, E.,
Lafrenière, D., Smalley, B., Southworth, J., 2013: Spitzer 3.6 and 4.5μm full-orbit
lightcurves of WASP-18, MNRAS, 428, 2645-2660.
Perez-Becker, D., Showman, A.P., 2013: Atmospheric heat redistribution on hot Jupiters,Astrophys. J., 776, 134.
Rauscher, E., Menou, K., 2012: A general circulation model for gaseous exoplanets withdouble-gray radiative transfer, Astrophys. J., 750, 96.
Showman, A.P., Fortney, J.J., Lewis, N.K., Shabram, M., 2013a: Doppler signatures of theatmospheric circulation on hot Jupiters, Astrophys. J., 762, 24.
Showman, A.P., Fortney, J.J., Lian, Y., Marley, M.S., Freedman, R.S., Knutson, H.A.,
Charbonneau, D., 2009: Atmospheric circulation of hot Jupiters: Coupled radiativedynamical general circulation model simulations of HD189733b and HD209458b,
Astrophys. J., 699, 564-584.
Showman, A.P., Guillot, T., 2002: Atmospheric circulation and tides of "51 Pegasus blike" planets, Astronom. and Astrophys., 385, 166-180.
Showman, A.P., Lewis, N.K., Fortney, J.J., 2015: Three-dimensional atmosphericcirculation of warm and hot Jupiters: Effects of orbital distance, rotation period, andnonsynchronous rotation, Astrophys. J., 801, 95.

References3
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Showman, A.P., Polvani, L.M., 2011: Equatorial superrotation on tidally locked
exoplanets, Astrophys. J., 738, 71.
Showman, A.P., Wordsworth, R.D., Merlis, T.M., Kaspi, Y., 2013b: Atmosphericcirculation of terrestrial exoplanets, Comparative Climatology of Terrestrial Planets, The
University of Arizona Press, 277-326.
Stevenson, K.B., Désert, J., Line, M.R., Bean, J.L., Fortney, J.J., Showman, A.P., Kataria,T., Kreidberg, L., McCullough, P.R., Henry, G.W., Charbonneau, D., Burrows, A., Seager,S., Madhusudhan, N., Williamson, M.H., Homeier, D., 2014: Thermal structure of an
exoplanet atmosphere from phase-resolved emission spectroscopy, Science, 346, 838-841.
Wong, I., Knutson, H.A., Kataria, T., Lewis, N.K., Burrows, A., Fortney, J.J., Schwartz, J.,Shporer, A., Agol, E., Cowan, N.B., 2016: 3.6 and 4.5 μm spitzer phase curves of thehighly irradiated hot jupiters WASP-19b and HAT-P-7b, Astrophys. J., 823, 122.
Zellem, R.T., Lewis, N.K., Knutson, H.A., Griffith, C.A., Showman, A.P., Fortney, J.J.,
Cowan, N.B., Agol, E., Burrows, A., Charbonneau, D., Deming, D., Laughlin, G.,
Langton, J., 2014: The 4.5μm full-orbit phase curve of the hot Jupiter HD209458b,Astrophys. J., 790, 53.
(p.2) http://www.esa.int/spaceinimages/Images/2003/06/Planet_transit(p.2) http://natgeo.nikkeibp.co.jp/nng/images/news/bigphotos/images/new-planet-infraredkeck-telescope_30112_big.jpg(p.3) http://exoplanet.eu/